Influence of Node Density in the Numerical Simulation of Water Hammer

Abstract

Water hammer is one of the most important fluid transient phenomena. The prediction of the pressure peak and wave shape is a fundamental task for the design of a fluid system. At DLR Lampoldshausen a new test-bench has been built in order to investigate water hammer and other fluid transient phenomena. The numerical model of the test-bench has been built by using the software EcosimPro® in conjunction with the ESPSS library, an ESA-developed tool capable of one dimensional, two-phase flow simulation in transient conditions. Several models are presented and the results are compared against experiments run with water. The water hammer pressure peak and frequency are well predicted while the damping of the water hammer wave shows a great discrepancy. It has been determined that the number of nodes plays a decisive role on the damping behavior. For this reason an intensive parametric study with different node numbers has been performed. By increasing the number of nodes the amplitude of the water hammer sinusoidal wave converges to a value that is almost 5 times higher than the experimental one, while a good damping can be achieved with a relative low number of nodes. This is due to the numerical damping, which is coupled with the nodes number. Setting the numerical damping almost to zero (a zero value would rise instabilities) shows in fact no physical damping dependency on the nodes density. A good agreement between numerical and experimental data can be reached, though the chosen model gives less accurate results when changing the boundary conditions such as flow velocity and valve closing time. Moreover, comparing the pressure at different positions of the test section, the discrepancy between the simulation and experiment increases with distance upstream of the valve (towards the tank). In addition to the node density, other parameters such as mathematical scheme, integration method, error and time step have been examined in order to reach a good compromise in terms of results accuracy and CPU time.